Related papers: Kernel-Cokernel Sequence for Composition and its A…
Let g be a semisimple Lie algebra over the complex numbers. Fix a positive integer l (called the level). Let R(l,g) be the fusion algebra at level l. Then, there is an algebra homomorphism from the representation ring R(g) of g to R(l,g).…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
Motivated by practical applications, I present a novel and comprehensive framework for operator-valued positive definite kernels. This framework is applied to both operator theory and stochastic processes. The first application focuses on…
We produce precise estimates for the Kogbetliantz kernel for the approximation of functions on the sphere. Furthermore, we propose and study a new approximation kernel, which has slightly better properties.
This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…
In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…
A convenient technique for calculating completed topological tensor products of functional Frechet or DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information,…
While direct statements for kernel based interpolation on regions $\Omega \subset \mathbb{R}^d$ are well researched, far less is known about corresponding inverse statements. The available inverse statements for kernel based interpolation…
The \textsc{$l$-Exact Component Order Connectivity} problem asks whether, given an input graph $G$ and an integer $k$, there exists a vertex subset $S\subseteq V(G)$ of size at most $k$ such that every connected component in $G - S$ has…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
We use relative group cohomologies to compute the Kac cohomology of matched pairs of finite groups. This cohomology naturally appears in the theory of abelian extensions of finite dimensional Hopf algebras. We prove that Kac cohomology can…
We construct a seven-term exact sequence involving low degree cohomology spaces of a Lie algebra $\Lg$, an ideal $\Lh$ of $\Lg$ and the quotient $\Lg / \Lh$ with coefficients in a $\Lg$-module. The existence of such a sequence follows from…
In abstract interpretation-based static analysis, approximation is encoded by abstract domains. They provide systematic guidelines for designing abstract semantic functions that approximate some concrete system behaviors under analysis. It…
In this paper, we show that a suitably chosen covariance function of a continuous time, second order stationary stochastic process can be viewed as a symmetric higher order kernel. This leads to the construction of a higher order kernel by…
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous convergence. To this end, we find the class of kernels and the structure of…
A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis Quadrature for Fredholm integral equations of the second kind, whose kernel is either discontinuous or not smooth along the main diagonal, is…
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…
Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.
During the last years, several algorithmic meta-theorems have appeared (Bodlaender et al. [FOCS 2009], Fomin et al. [SODA 2010], Kim et al. [ICALP 2013]) guaranteeing the existence of linear kernels on sparse graphs for problems satisfying…